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Ch.18 - Chemistry of the Environment
All textbooksBrown 14th EditionCh.18 - Chemistry of the EnvironmentProblem 83
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Chapter 18, Problem 83

Bioremediation is the process by which bacteria repair their environment in response, for example, to an oil spill. The efficiency of bacteria for 'eating' hydrocarbons depends on the amount of oxygen in the system, pH, temperature, and many other factors. In a certain oil spill, hydrocarbons from the oil disappeared with a first-order rate constant of 2 * 10 s. At that rate, how many days would it take for the hydrocarbons to decrease to 10% of their initial value?

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1
Identify that the problem involves first-order kinetics, which can be described by the equation: \( [A] = [A]_0 e^{-kt} \), where \([A]\) is the concentration at time \(t\), \([A]_0\) is the initial concentration, \(k\) is the rate constant, and \(t\) is time.
Recognize that the problem asks for the time it takes for the concentration to decrease to 10% of its initial value, meaning \([A] = 0.1[A]_0\).
Substitute \([A] = 0.1[A]_0\) into the first-order kinetics equation: \( 0.1[A]_0 = [A]_0 e^{-kt} \).
Simplify the equation by dividing both sides by \([A]_0\), resulting in \( 0.1 = e^{-kt} \).
Take the natural logarithm of both sides to solve for \(t\): \( \ln(0.1) = -kt \). Substitute the given rate constant \(k = 2 \times 10^{-1} \text{s}^{-1}\) and solve for \(t\) in seconds, then convert \(t\) to days.
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Textbook Question

The water supply for a midwestern city contains the following impurities: coarse sand, finely divided particulates, nitrate ions, trihalomethanes, dissolved phosphorus in the form of phosphates, potentially harmful bacterial strains, dissolved organic substances. Which of the following processes or agents, if any, is effective in removing each of these impurities: coarse sand filtration, activated carbon filtration, aeration, ozonization, precipitation with aluminum hydroxide?

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Textbook Question

An impurity in water has an extinction coefficient of 3.45⨉103 M-1 cm-1 at 280 nm, its absorption maximum (A Closer Look, p. 576). Below 50 ppb, the impurity is not a problem for human health. Given that most spectrometers cannot detect absorbances less than 0.0001 with good reliability, is measuring the absorbance of a water sample at 280 nm a good way to detect concentrations of the impurity above the 50-ppb threshold?

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Textbook Question

The concentration of H2O in the stratosphere is about 5 ppm. It undergoes photodissociation according to: H2O1g2 ¡ H1g2 + OH1g2 (b) Using Table 8.3, calculate the wavelength required to cause this dissociation.

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Open Question
The standard enthalpies of formation of ClO and ClO2 are 101 and 102 kJ/mol, respectively. Using these data and the thermodynamic data in Appendix C, calculate the overall enthalpy change for each step in the following catalytic cycle: ClO(g) + O(g) → ClO(g) + O(g). What is the enthalpy change for the overall reaction that results from these two steps?
Open Question
The main reason that distillation is a costly method for purifying water is the high energy required to heat and vaporize water. (a) Using the density, specific heat, and heat of vaporization of water from Appendix B, calculate the amount of energy required to vaporize 1.00 gal of water beginning with water at 20 °C. (b) If the energy is provided by electricity costing $0.085/kWh, calculate its cost. (c) If distilled water sells in a grocery store for $1.26 per gal, what percentage of the sales price is represented by the cost of the energy?
Open Question
A reaction that contributes to the depletion of ozone in the stratosphere is the direct reaction of oxygen atoms with ozone: O(g) + O3(g) → 2 O2(g). At 298 K, the rate constant for this reaction is 4.8 × 10⁵ M⁻¹ s⁻¹. Would you expect this reaction to occur via a single elementary process? Explain why or why not.